Gravitational Fields Topic 6 1 Gravitational Force What

Gravitational Fields Topic 6. 1

Gravitational Force � What are the variables that affect the gravitational force on an object? � It was found (discovered? )that : Compare with: Sir Issac Newton (1642 – 1727) What are the major differences?

Newton’s Law of Universal Gravitation

Newton’s law of universal gravitation For large objects like the earth, r is the distance to the centre of mass

Calculations using Newton’s law What is the force of attraction between Andrei and Mike? 7. 3 x 10 -8 N 2 m 63 kg ? 70 kg ?

Force of gravity due to earth on Mike? 615 N 63 kg ? (Mike’s weight) R = 6400 km, m = 6 x 1024 kg

Force of gravity due to earth on Michael? F = Gm 1 m 2 = 6. 667 x 10 -11 x 63 x 6 x 1024 = 615 N (= mg) r 2 (6400 x 103)2 In other words, for any planet; g = Gmp r p 2

Gravitational field An area or region where a mass feels a gravitational force is called a gravitational field. The gravitational field strength at any point in space is defined as the force per unit mass (on a small test mass) at that point. g = F/m (in N. kg-1)

Gravitational field around a point mass If we have two masses m 1 and m 2 distance r apart F = Gm 1 m 2/r 2 m 1 m 2 Looking at the force on m 1 due to m 2, F = gm 1 F = Gm 1 m 2/r 2 = gm 1 g (field due to m 2) = Gm 2/r 2

Gravitational field around a point I told you, for any mass planet; If we have two masses m 1 and m 2 distance r apart g = Gmp F = Gm 1 m 2/r 2 r p 2 m 2 for a Don’t forget that nontopoint Looking at the force on m 1 due m 2, Fmass, = gmr 1 is the distance to the centre of mass F = Gm 1 m 2/r 2 = gm 1 g (field due to m 2) = Gm 2/r 2

Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition. Field here due to both masses? m 1 m 2

Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition. Field due to m 1 Field here due to both masses? m 2

Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition. Field due to m 1 Field due to m 2

Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition. Field due to m 1 Field due to m 2 Resultant Field m 1 m 2

Gravitational field patterns A gravitational field can be represented by lines and arrows on a diagram, in a similar ways to magnetic field lines.

Gravitational field patterns A gravitational field can be represented by lines and arrows on a diagram, in a similar ways to magnetic field lines. The closer the lines are together, the stronger the force felt. This is an example of a radial field Note, gravity is ALWAYS attractive

Field around a charged metal sphere E = 0 inside the sphere

Field around a uniform spherical mass

Field close to the earth’s surface Uniform